Technique for quantiating biological markers using quantum resonance interferometry

ABSTRACT

A technique is described for quantitating biological indicators, such as viral load, using interferometric interactions such as quantum resonance interferometry. A biological sample is applied to an array information structure that has a plurality of elements that emit data indicative of viral load. A digitized output pattern of the arrayed information structure is interferometrically enhanced by generating interference between the output pattern and a reference wave. The interferometrically enhanced output pattern is then analyzed to identify emitted data indicative of viral load which in turn is used to determine viral load.

RELATED APPLICATION

This application is a Continuation of U.S. patent application Ser. No.09/523,539 entitled “Method and System for Quantitation of Viral LoadUsing Microarrays” filed Mar. 10, 2000, which is a Continuation of U.S.patent application Ser. No. 09/253,791, now U.S. Pat. No. 6,245,511,entitled “Method and Apparatus for Exponentially Convergent TherapyEffectiveness Monitoring Using DNA Microarray Based Viral LoadMeasurements” filed Feb. 22, 1999.

FIELD OF THE INVENTION

The invention generally relates to techniques for monitoring theeffectiveness of medical therapies and dosage formulations, and inparticular to techniques for monitoring therapy effectiveness usingviral load measurements.

BACKGROUND OF THE INVENTION

It is often desirable to determine the effectiveness of therapies, suchas those directed against viral infections, including therapiesinvolving individual drugs, combinations of drugs, or other relatedtherapies. One conventional technique for monitoring the effectivenessof a viral infection therapy is to measure and track a viral loadassociated with the viral infection, wherein the viral load is ameasurement of a number of copies of the virus within a given quantityof blood, such per milliliter of blood. The therapy is deemed effectiveif the viral load is decreased as a result of the therapy. Adetermination of whether any particular therapy is effective is helpfulin determining the appropriate therapy for a particular patient and alsofor determining whether a particular therapy is effective for an entireclass of patients. The latter is typically necessary in order to obtainFDA approval of any new drug or medical device therapy. Viral loadmonitoring is also useful for research purposes such as for assessingthe effectiveness of new antiviral compounds determine, for example,whether it is useful to continue developing particular antiviralcompounds or to attempt to gain FDA market approval.

A test to determine the viral load can be done with blood drawn fromT-cells or from other standard sources. The viral load is typicallyreported either as an absolute number, i.e., the number of virusparticles per milliliter of blood or on a logarithmic scale. Likewise,decreases in viral load are reported in absolute numbers, logarithmicscales, or as percentages.

It should be noted though that a viral load captures only a fraction ofthe total virus in the body of the patient, i.e., it tracks only thequantity of circulating virus. However, viral load is an importantclinical marker because the quantity of circulating virus is the mostimportant factor in determining disease outcome, as changes in the viralload occur prior to changes in other detectable factors, such as CD4levels. Indeed, a measurement of the viral load is rapidly becoming theacceptable method for predicting clinical progression of certaindiseases such as HIV.

Insofar as HIV is concerned, HIV-progression studies have indicated asignificant correlation between the risk of acquiring AIDS and aninitial HIV baseline viral load level. In addition to predicting therisk of disease progression, viral load testing is useful in predictingthe risk of transmission. In this regard, infected individuals withhigher viral load are more likely to transmit the virus than others.

Currently, there are several different systems for monitoring viral loadincluding quantitive polymerase chain reaction (PCR) and nucleic acidhybridization. Herein, the term viral load refers to any virologicalmeasurement using RNA, DNA, or p24 antigen in plasma. Note that viralRNA is a more sensitive marker than p24 antigen. p24 antigen has beenshown to be detectable in less than 50% asymptomatic individuals.Moreover, levels of viral RNA rise and fall more rapidly than levels ofCD4+ lymphocytes. Hence, changes in infection can be detected morequickly using viral load studies based upon viral RNA than using CD4studies. Moreover, viral load values have to date proven to be anearlier and better predictor of long term patient outcome than CD4-cellcounts. Thus, viral load determinations are rapidly becoming animportant decision aid for anti-retro viral therapy and diseasemanagement. Viral load studies, however, have not yet completelyreplaced CD+ analysis in part because viral load only monitors theprogress of the virus during infection whereas CD4+ analysis monitorsthe immune system directly. Nevertheless, even where CD4+ analysis iseffective, viral load measurements can supplement information providedby the CD4 counts. For example, an individual undergoing long termtreatment may appear stable based upon the observation of clinicalparameters and CD4 counts. However, the viral load of the patient maynevertheless be increasing. Hence, a measurement of the viral load canpotentially assist a physician in determining whether to change therapydespite the appearance of long term stability based upon CD4 counts.

Thus, viral load measurements are very useful. However, there remainsconsiderable room for improvement. One problem with current viral loadmeasurements is that the threshold level for detection, i.e., the nadirof detection, is about 400-500 copies per milliliter. Hence, currently,if the viral load is below 400-500 copies per milliliter, the virus isundetectable. The virus may nevertheless remain within the body. Indeed,considerable quantities of the virus may remain within the lymph system.Accordingly, it would be desirable to provide an improved method formeasuring viral load which permits viral load levels of less than400-500 copies per milliliter to be reliably detected.

Another problem with current viral load measurement techniques is thatthe techniques are typically only effective for detecting exponentialchanges in viral loads. In other words, current techniques will onlyreliably detect circumstances wherein the viral load increases ordecreases by an order of magnitude, such by a factor of 10. In othercases, viral load measurements only detect a difference betweenundetectable levels of the virus and detectable levels of the virus. Ascan be appreciated, it would be highly desirable to provide an improvedmethod for tracking changes in viral load which does not require anexponential change in the viral load for detection or which does notrequire a change from an undetectable level to a detectable level.Indeed, with current techniques, an exponential or sub-exponentialchange in the viral load results only in a linear change in theparameters used to measure the viral load. It would instead be highlydesirable to provide a method for monitoring the viral load whichconverts a linear change in the viral load into an exponential changewithin the parameters being measured to thereby permit very slightvariations in viral load to be reliably detected. In other words,current viral load detection techniques are useful only as a qualitativeestimator, rather than as a quantative estimator.

One reason that current viral load measurements do not reliably tracksmall scale fluctuations in the actual number of viruses is that asignificant uncertainty in the measurements often occurs. As a result,individual viral load measurements have little statistical significanceand a relatively large number of measurements must be made before anystatistically significant conclusions can be drawn. As can beappreciated it would be desirable to provide a viral load detectiontechnique which can reliably measure the viral load such that thestatistical error associated with a single viral load measurement isrelatively low to permit individual viral load measurements to be moreeffectively exploited.

Moreover, because individual viral load measurements are notparticularly significant when using current methods, treatment decisionsfor individual patients based upon the viral load measurements must bebased only upon long term changes or trends in the viral load resultingin a delay in any decision to change therapy. It would be highlydesirable to provide an improved method for measuring and tracking viralload such that treatment decisions can be made much more quickly basedupon short term trends of measured viral load.

As noted above, the current nadir of viral load detectability is at400-500 copies of the virus per milliliter. Anything below that level isdeemed to be undetectable. Currently the most successful and potentmulti-drug therapies are able to suppress viral load below that level ofdetection in about 80-90 percent of patients. Thereafter, viral load isno longer an effective indicator of therapy. By providing a viral loadmonitoring technique which reduces the nadir of detectabilitysignificantly, the relative effectiveness of different multi-drugtherapies can be more effectively compared. Indeed, new FDA guidelinesfor providing accelerated approval of a new drug containing regimenrequires that the regimen suppress the viral load below the currentnadir of detection in about 80 to 85 percent of cases. If the newregimen suppresses the viral load to undetectable levels in less than 80to 85 percent of the cases, the new drug will gain accelerated approvalonly if it has other redeeming qualities such as a preferable dosingregimen (such as only once or twice per day), a favorable side effectprofile, or a favorable resistance or cross-resistance profile. Thus,the ability of a regimen to suppress the viral load below the level ofdetection is an important factor in FDA approval. However, because thelevel of detectability remains relatively high, full approval iscurrently not granted by the FDA solely based upon the ability of theregimen to suppress the viral load below the minimum level of detection.Rather, for full approval, the FDA may require a further demonstrationof the durability of the regimen, i.e., a demonstration that the drugregimen suppresses the viral load below the level of detectability andkeeps it below the level of detectability for some period of time.

As can be appreciated, if a new viral load measurement and trackingtechnique were developed which could reliably detect viral load atlevels much lower than the current nadir of detectability, the FDA maybe able, using the new technique, to much more precisely determine theeffectiveness of a drug regimen for the purposes of granting approvalsuch that a demonstration of the redeeming evalities will no longer benecessary.

For all of these reasons, it would be highly desirable to provide animproved technique for measuring and tracking viral load capable ofproviding much more precise and reliable estimates of the viral load andin particular capable of reducing the nadir of detectabilitysignificantly. The present invention is directed to this end.

SUMMARY OF THE INVENTION

In accordance with a first aspect of the invention, a method is providedfor determining the effectiveness of a therapy, such as an anti-viraltherapy, by analyzing biochip output patterns generated from biologicalsamples taken at different sampling times from a patient undergoing thetherapy. In accordance with the method, a viral diffusion curveassociated with a therapy of interest is generated and each of theoutput patterns representative of hybridization activity is then mappedto coordinates on the viral diffusion curve using fractal filtering. Adegree of convergence between the mapped coordinates on the viraldiffusion curve is determined. Then, a determination is made as towhether the therapy of interest has been effective based upon the degreeof convergence.

In an exemplary embodiment, the viral diffusion curve is spatiallyparameterized such that samples map to coordinates near the curvemaxima, if the viral load is increasing (i.e., therapy or dosage isineffective). In this manner, any correlation between rate and extent ofconvergence across different patient samples is exploited to provide aquantitative and qualitative estimate of therapy effectiveness.

Also in the exemplary embodiment, the biological sample is a DNA sample.The output pattern of the biochip is quantized as a dot spectrogram. Theviral diffusion curve is generated by inputting parametersrepresentative of viral load studies for the therapy of interest,generating a preliminary viral diffusion curve based upon the viral loadstudies; and then calibrating a degree of directional causality in thepreliminary viral diffusion curve to yield the viral diffusion curve.The parameters representative of the viral load studies include one ormore of baseline viral load (BVL) set point measurements at whichdetection is achieved, BVL at which therapy is recommended and viralload markers at which dosage therapy is recommended. The step ofgenerating the preliminary viral diffusion curve is performed byselecting a canonical equation representative of the viral diffusioncurve, determining expectation and mean response parameters for use inparameterizing the equation selected to represent the viral diffusioncurve and parameterizing the equation selected to represent the viraldiffusion curve to yield the preliminary viral diffusion curve.

Also, in the exemplary embodiment, each dot spectrogram is mapped to theviral diffusion curve using fractal filtering by generating apartitioned iterated fractal system IFS model representative of the dotspectrogram, determining affine parameters for IFS model, and thenmapping the dot spectrogram onto the viral diffusion curve using theIFS. Before the dot spectrograms is mapped to the viral diffusion curve,the dot spectrograms are interferometrically enhanced. After themapping, any uncertainty in the mapped coordinates is compensated forusing non-linear information filtering.

In accordance with a second aspect of the invention, a method isprovided for determining the viral load within a biological sample byanalyzing an output pattern of a biochip to which the sample is applied.In accordance with the method, a viral diffusion curve associated with atherapy of interest is generated and then calibrated using at least twoviral load measurements. Then the output pattern for the sample ismapped to coordinates on the calibrated viral diffusion curve usingfractal filtering. The viral load is determined from the calibratedviral diffusion curve by interpreting the coordinates of the viraldiffusion curve.

Apparatus embodiments are also provided. By exploiting aspects of theinvention, disease management decisions related to disease progression,therapy and dosage effectiveness may be made by tracking the coordinateson the viral diffusion curve as successive DNA-/RNA-based microarraysamples are collected and analyzed.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, objects, and advantages of the present invention willbecome more apparent from the detailed description set forth below whentaken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

FIG. 1 is a flow chart illustrating an exemplary method for determiningthe effectiveness of a viral therapy in accordance with the invention.

FIG. 2 is a flow chart illustrating an exemplary method for generatingViral Diffusion Curves for use with the method of FIG. 1.

FIG. 3 is a flow chart illustrating an exemplary method for mapping dotspectrograms onto Viral Diffusion Curves using fractal filtering for usewith the method of FIG. 1.

FIG. 4 is a block diagram illustrating the effect of the fractalfiltering of FIG. 3.

FIG. 5 is a flow chart illustrating an exemplary method for compensatingfor uncertainty using non-linear information filtering for use with themethod of FIG. 1.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

With reference to the figures, exemplary method embodiments of inventionwill now be described. The exemplary method will be described primarilywith respect to the determination of changes in viral loads based uponthe output patterns of a hybridized biochip microarray using DNAsamples, but principles of the invention may be applied to otherprotein-based samples or to other types of output patterns as well.

With reference to FIG. 1, steps will be described for generating viraldiffusion curves for use is processing DNA biomicroarray output patternsto determine the effectiveness of therapies imposed upon a patientproviding samples for which the outputs are generated. Then, steps willbe described for processing the specific output patterns using theVDC's.

An underlying clinical hypothesis of the exemplary method is thatantiviral treatment should inhibit viral replication and lower anindividual's viral load from baseline or suppress rising values. Astationary or rising viral load after the introduction of antiviraltherapy indicates a lack of response to the drug(s) or the developmentof drug resistance. The VDC exploits the underlying hypothesis in partby correlating the rate of disease progression to a sample point valuesuch that a change in sample point indicates progression.

The Method

At step 100, parameters representative of viral load studies for thetherapy of interest are input. A preliminary viral diffusion curve isgenerated, at step 102, based upon the viral load studies. Theparameters representative of the viral load studies include baselineviral load (BVL) set point measurements at which detection is achieved,BVL at which therapy is recommended and viral load markers at whichdosage therapy is recommended. At step 104, a degree of directionalcausality in the preliminary viral diffusion curve is calibrated toyield the final viral diffusion curve.

Steps 100-104 are performed off-line for setting up the VDC's. Thesesteps need be performed only once for a given therapy and for a givenset of baseline viral load measurements. Thereafter, any number of DNAbiomicroarray output patterns may be processed using the VDC's todetermine the effectiveness of the therapy. Preferably, VDC's aregenerated for an entire set of therapies that may be of interest suchthat, for any new DNA biomicroarray output pattern, the effectiveness ofany of the therapies can be quickly determined using the set of VDC's.In general, the aforementioned steps need be repeated only to update theVDC's based upon new and different baseline viral load studies or if newtherapies of interest need to be considered.

In the following, steps will be summarized for processing DNAbiomicroarray output patterns using the VDC's to determine whether anytherapies of interest represented by the VDC's are effective. Todetermine the effectiveness of therapy at least two samples of DNA to beanalyzed are collected from a patient, preferably taken some time apart,and biomicroarray patterns are generated therefrom. In other casesthough, the different samples are collected from different patients.

The output patterns for the DNA biomicroarray are referred to herein asdot spectrograms. A dot spectrogram is generated using a DNAbiomicroarray for each sample from an N by M DNA biomicroarray. Anelement of the array is an “oxel”: o(i,j). An element of the dotspectrogram is a hixel: h(i,j). The dot spectrogram is represented bycell amplitudes given by Φ(i,j) for i:1 to N, and j:1 to M.

Dot spectrograms are generated from the samples taken at different timesusing a prefabricated DNA biomicroarray at step 106. The dotspectrograms are interferometrically enhanced at step 108. Each dotspectrogram is then mapped to coordinates on the viral diffusion curvesusing fractal filtering at step 110. After the mapping, any uncertaintyin the mapped coordinates is compensated for at step 112 usingnon-linear information filtering.

VDC coordinates are initialized at step 114, then updated in accordancewith filtered dot spectrograms at step 116. A degree of convergencebetween the mapped coordinates on the viral diffusion curves is thendetermined at step 118 and a determination is made as to whether thetherapy of interest has been effective. The determination is based uponwhether the degree of convergence increases from one DNA sample toanother. An increase in degree of convergence is representative of alack of effectiveness of the therapy of interest. Hence, if the degreeof convergence decreases, then execution proceeds to step 120, wherein asignal is output indicating that the therapy is effective. If the degreeof convergence increases, then execution proceeds to step 122 whereinVDC temporal scale matching is performed. Then a determination is madeat step 124 whether an effectiveness time scale has been exceeded. Ifexceeded, then a conclusion is drawn that the effectiveness of the viraltherapy cannot be established even if more samples are analyzed. If notexceeded, then execution returns to step 106 wherein another sampletaken from the same patient at a latter time is analyzed by repeatingsteps 106 through 118.

Viral Load Studies

Viral load studies for therapies of interest are parameterized at step100 as follows. The therapy of interest is selected from a predeterminedlist of therapies for which viral load studies have been performed.Measurements from viral load studies are input for therapy of interest.As noted, the viral load measurements include one or more of BaselineViral Load (BVL) set point measurements at which detection is achieved;BVL at which therapy is recommended; and VL markers at which dosagechange recommended.

Data for the viral load measurements are obtained, for example, fromdrug qualification studies on a minimum include dosages, viral limits aswell as time cycles within which an anti-viral drug is deemed effective.The data is typically qualified with age/weight outliners and patienthistory. Attribute relevant to this claim is the γ₁ or BVL_(LOW) whichcorresponds to the lowest detection limit shown for a therapy to beeffective using conventional assays or any other diagnostic means.BVL_(NP-LOW) denotes the lowest threshold at which viral load isachieved using a nucleotide probe. Using interferometric enhancementtechnique, BVL_(NP-LOW <<)BVL_(LOW).

Generation of Viral Diffusion Curves

Referring now to FIG. 2, the viral diffusion curves are generated asfollows. An equation is selected for representing the VDC at step 200.Expectation (μ) and mean response parameters are determined at step 202for use in parameterizing the selected equation. Then the equationselected to represent the VDC is parameterized at step 204 to yield anumerical representation of the VDC. These steps will now be describedin greater detail.

These steps populate a canonical machine representation, denoted asVDC(i, Γ, γ, κ) (which is a special case of Fokker-Planck equation) tocalibrate responses from a viral load detection DNA-array basedhybridization biomicroarray.

i is the index for a diagnostic condition/therapy of interest,

Γ denotes the parameter vector characterizing the VDC,

λ denotes the clinical endpoints vector that indicates detectabilitythresholds for a specific DNA-hybridization array implementation

κ correspond to the uncertainty interval estimates.

An example of an equation selected for representing the VDC is:${\frac{\partial\rho}{\partial t} = {{{div}\left( {{\nabla{\Psi (x)}}\rho} \right)} + \frac{\Delta\rho}{\beta}}},\quad {{\rho \left( {x,0} \right)} = {\rho^{0}(x)}}$

The potential Ψ(x): R^(n)→[0, ∞) is a smooth function, β>0 is selectedconstant, and ρ⁰ (x) is a probability density on R^(n).

Preferably, the diffusion potential of the equation and the BVL data aresuch that:

Ψ(x)<c[BVL _(NP) _(—) _(LOW) |BVL _(LOW)]

the constant c is generally set to$c = \frac{\left\lbrack {{number}\quad {of}\quad {amplitude}\quad {discretization}\quad {levels}} \right\rbrack}{\begin{matrix}\left\lbrack {{\log\left( {{PCR}\quad {amplification}\quad {factor}} \right)}*{avg}\text{(}{{oligonucleotides}/{oxel}}\text{)}*} \right. \\\left. {\left\lceil {{tagging}\quad {efficiency}} \right\rceil*\left\lfloor {{binding}\quad {efficiency}} \right\rfloor} \right\rbrack\end{matrix}}$

Binding efficiency is difficult to quantify analytically for abiomicroarray device technology. Hence, for use in the above equation,an estimate of the binding efficiency is preferably employed. A bindingefficiency of 30% (0.3) is appropriate, though other values mayalternatively used. Depending upon the specific biomicroarray used, theconstant c typically ranges between 0.0001 to 0.5.

Expectation and Mean Response Parameters

The expectation (μ) and mean response parameters are then determined atstep 202 for use in parameterizing the equation selected to representthe VDC. The expectation and mean response values are determined by: 1)performing conventional PCR amplification; 2) obtaining calibrated viralcounts from the PCR amplification; 3) determining enhanced andnormalized hybridization amplitude mean and variance valuescorresponding to the calibrated viral counts; and 4) matching theenhanced and normalized hybridization amplitude mean and variancevalues.

Two synthetic amplification techniques (in addition to PCR and anydesigner tagging) are used to achieve VL estimation above the BVL limitset for the exemplary embodiment of the method, namely (a) readoutpre-conditioning, and (b) nonlinear interferometric enhancement.Moreover, the expectation match condition implies that:$\frac{\begin{matrix}{{Expectation}\quad\left\lbrack {Log} \right.} \\\left. \left( \left\lfloor {{interferometrically}\quad {enhanced}\quad {image}} \right\rfloor \right) \right\rbrack_{\quad {\bigvee\quad {\lbrack{{expression}\quad {set}\quad {of}\quad {interest}}\rbrack}}}\end{matrix}}{\begin{matrix}{Expectation} \\\left\lbrack {{preconditioned}\quad {image}\quad {amplitude}} \right\rbrack_{\quad {\bigvee{\lbrack{{expression}\quad {set}\quad {of}\quad {interest}}}}}\end{matrix}} \cong 1$

Variance matching is done similarly with respect to biomicroarrayreadout. The lower bound of mean response value can be given by:$\frac{\begin{matrix}{{Variance}\quad\left\lbrack {Log} \right.} \\\left. \quad \left( \left\lfloor {{interferometrically}\quad {enhanced}\quad {image}} \right\rfloor \right) \right\rbrack_{\quad {\bigvee\quad {\lbrack{{expression}\quad {set}\quad {of}\quad {interest}}\rbrack}}}\end{matrix}}{\begin{matrix}{Variance} \\\left\lbrack {{preconditioned}\quad {image}\quad {amplitude}} \right\rbrack_{\quad {\bigvee\quad {\lbrack{{expression}\quad {set}\quad {of}\quad {interest}}}}}\end{matrix}} \cong 1$

Using the above expression, a conservative lower bound forinterferometric enhancement is estimated for each nucleotide expressionof interest. Since the array fabrication device is assumed to have (i)an identical oligonucleotide density per oxel and (ii) equal lengtholigonucleotides, the same mean response amplitude can be assumed. Ifthese two assumptions are not met then bounds need to be individuallycalculated and averaged using the above formula. Another assumption isthat the binding efficiency is statistically independent of the actualoligonucleotide sequence. If this assumption does not hold for thespecific device technology then the binding efficiency should beprovided as well for each expressed sequence of interest. So thecomputational analysis method uses the analytically derived lowerbounds, as computed using the above equation. This is a one-timecalculation only and is done offline at design time.

Parameterization of the VDC

The equation selected to represent the VDC is then parameterized usingthe expectation and mean response values at step 204 to yield anumerical representation of the VDC using

 y(x)=β₀+β₁ x+β ₂ x ²

subject to constraints$\overset{.}{x} = {{\gamma \quad {\sin^{k}\left\lbrack {\frac{\sqrt{\omega}}{\alpha}\left( {\beta_{0} + {\beta_{1}x} + {\beta_{2}x^{2}}} \right)} \right\rbrack}\quad \sin \quad \omega \quad t} + {ɛ(t)}}$

with constants α, β, γ and ε<<1.

This utility of this parameterization is established as follows. The VDCcanonical representation is based on a variational formulation of theFokker-Planck. The Fokker-Planck (FP) equation, or forward Kolmogorovequation, describes the evolution of the probability density for astochastic process associated with an Ito stochastic differentialequation. The exemplary method exploits the VDC to model a physicaltime-dependent phenomena in which randomness plays a major role. Thespecific variant used herein is one for which the drift term is given bythe gradient of a potential. For a broad class of potentials (thatcorrespond to statistical variability in therapy response), a timediscrete, iterative variational is constructed whose solutions convergeto the solution of the Fokker-Planck equation. The time-step is governedby the Wasserstein metric on probability measures. In this formulationthe dynamics may be regarded as a gradient flux, or a steepest descentfor the free energy with respect to the Wasserstein metric. Thisparameterization draws from theory of stochastic differential equations:wherein a (normalized) solution to a given Fokker-Planck equationrepresents the probability density for the position (or velocity) of aparticle whose motion is described by a corresponding Ito stochasticdifferential equation (or Langevin equation). The drift coefficient is agradient. The method exploits “designer conditions” on the drift anddiffusion coefficients so that the stationary solution of aFokker-Planck equation satisfies a variational principle. It minimizes acertain convex free energy functional over an appropriate admissibleclass of probability densities.

A physical analogy is to an optimal control problem which is related tothe heating of a probe in a kiln. The goal is to control the heatingprocess in such a way that the temperature inside the probe follows acertain desired temperature profile. The biomolecular analogy is to seeka certain property in the parameterized VDC—namely, an exponential jumpin the VDC coordinate position for “small linear changes in the viralcount”.

This method is in contradistinction to conventional calibrationstrategies which obtain a linear or superlinear shift in quantizationparameter for an exponential shift in actual viral count.

As noted, the form of FP equation chosen is${\frac{\partial\rho}{\partial t} = {{{div}\left( {{\nabla{\Psi (x)}}\rho} \right)} + \frac{\nabla\rho}{\beta}}},\quad {{\rho \left( {x,0} \right)} = {\rho^{0}(x)}}$

where the potential Ψ(x): R^(n)→[0, ∞) is a smooth function, β>0 isselected constant, and ρ⁰ (x) is a probability density on R^(n). Thesolution ρ(t,x) is a probability density on R^(n) for almost every fixedtime t. So the distribution ρ(t,x)≧0 for almost every (t,x)∈ (0,∞) XR^(n), and ∫_(^(n))ρ(t, x)x = 1

for almost every t, ∈ (0,∞).

It is reasonably assumed that hybridization array device physics for theDNA biomicroarray (i.e., corresponding to the potential ψ) has anapproximately linear response to the nucleotide concentration and theresponse is monotonic with bounded drift. So,${\rho_{s}(x)} = {\frac{1}{Z}^{({- {{\beta\Psi}{(x)}}})}}$

where the partition function Z is given byZ = ∫_(^(n))^((−βΨ(x)))x

In this model the basis for device physics design is that the potentialneeds to be modulated such that it grows rapidly enough for Z to befinite. This is not achieved by conventional methods. However, atechnique which does achieve this result is described in co-pending U.S.patent application Ser. No. 09/253,789, now U.S. Pat. No. 6,136,541filed contemporaneously herewith, entitled “Method and Apparatus forAnalyzing Hybridized DNA Microarray Patterns Using Resonant InteractionsEmploying Quantum Expressor Functions”, which is incorporated byreference herein.

The probability measure ρ_(s)(x)dx is the unique invariant measure forthe Markov random field (MRF) fit to the empirical viral load data.

The method exploits a special dynamical effect to design ρ. The methodrestricts the FP equation form above to a more restricted case: randomwalk emulating between critical equilibrium points.

To aid in understanding this aspect of the invention, consider thediffusion form$\frac{\partial{\rho \left( {x,t} \right)}}{\partial t} = {\frac{1}{2}D^{2}\frac{\partial^{2}{\rho \left( {x,t} \right)}}{\partial^{2}t}}$

where D²=πα²

and α is constant.

A specific VDC shape is parameterized by:

y(x)=β₀+β₁ x+β ₂ x ²

subject to constraints$\overset{.}{x} = {{\gamma \quad {\sin^{k}\left\lbrack {\frac{\sqrt{\omega}}{\alpha}\left( {\beta_{0} + {\beta_{1}x} + {\beta_{2}x^{2}}} \right)} \right\rbrack}\quad \sin \quad \omega \quad t} + {ɛ(t)}}$

with constants α, β, γ and ε<<1.

These constants are set based upon the dynamic range expected for theviral load. Thus, if the viral load is expected to vary only within afactor of 10, the constants are set accordingly. If the viral load isexpected to vary within a greater range, different constants areemployed. The actual values of the constants also depend upon theparticular disease.

Where the following conditions are metExpectation  match:  E(x) = ∫_(−∞)^(∞)xf(x)x = μVariance:  σ² = ∫_(−∞)^(∞)(x − μ)²f_(x)xAnd  ∫_(−∞)^(∞)f(x) = 1

The expectation and mean response parameters for use in these equationsare derived, as described above, from matching the enhanced andnormalized hybridization amplitude mean and variance that correspond tocalibrated viral counts (via classical PCR amplification).

A distribution represented by the above-equations then satisfies thefollowing form with a prescribed probability distribution$\overset{.}{x} = {{\gamma \quad {\sin^{k}\left\lbrack {\frac{\sqrt{\omega}}{\alpha}{y(x)}} \right\rbrack}\quad \sin \quad \omega \quad t} + {ɛ(t)}}$${{{Assuming}\text{:~~}y^{\prime}} = {\frac{y}{x} > \beta > 0}},\quad {\beta = {constant}}$

and ε(t)=ε₀ay

such that

{dot over (a)}=a ^(1/3)(y−1)(y+1)−ε₀ a

and the distribution controlling equation is

f(x)=0.5|y′(x)|

such that y(−1)<X<y(1).

The characteristic timescale of response for this system is given by$T^{*} = {\frac{1}{\omega}{\arccos \quad\left\lbrack {1 - {\frac{B\left( {{1/3},{1/3}} \right)}{\sqrt[3]{2}}\frac{\alpha \sqrt{\omega}}{\gamma}}} \right\rbrack}}$

the successive points must show a motion with characteristic timescale.The VDC is designed such that sampling time falls well withincharacteristic time.

As noted the actual information used for populating above the parametersis available from the following: Baseline viral load (BVL) set pointmeasurements at which detection is achieved; BVL at which therapy isrecommended; and VL markers at which dosage change recommended.

The following provides an example of preclinical data that is availableto to assist in parameterizing the VDC.

NOTIONAL VIRAL LOAD MANAGEMENT EXAMPLE

This is a synthetic example to illustrate how data from clinical studiesmay be used to calibrate the VDC.

Viral Load analysis studies, using conventional assays, in HIVprogression have shown that neither gender, age, HCV co-infection, pasthistory of symptomatic HIV-1 infection, duration of HIV-1 infection norrisk group are associated with a higher risk of increasing baselineviral load (BVL) to the virologic end-point. However, patients with ahigh (BVL) between 4000-6000 copies had a 10-fold higher risk ofincreasing the level of viral load than patients with a BVL below 1500copies/ml. Thus, baseline viral load set point measurements provide animportant indicator for onset of disease.

Initiation of antiretroviral therapy is generally recommended when theCD4⁺ T-cell count is <600 cells/mL and the viral load level is >6,000copies/mL. When the viral load is >28000 copies/mL, initiation oftherapy is recommended regardless of other laboratory markers andclinical status.

Effective antiretroviral treatment may be measured by changes in plasmaHIV RNA levels. The ideal end point for effective antiviral therapy isto achieve undetectable levels of virus (<400 copies/mL). A decrease inHIV RNA levels of at least 0.5 log suggests effective treatment, while areturn to pretreatment values (±0.5 log) suggests failure of drugtreatment.

When HIV RNA levels decline initially but return to pretreatment levels,the loss of therapy effectiveness has been associated with the presenceof drug-resistant HIV strains.

The therapy-specific preclinical viral load markers (such as low andhigh limits in the above example) are used to establish actual BVLboundaries for the VDC associated with a particular therapy. In thisregard, the determination of the BVL parameters is disease specific. Forexample, in HIV methods such as RT-PCR, bDNA or NASBA are used. Otherdiseases use other assays. Typically, once the parameters of the VDCequation have been set (i.e. constants α, β, γ and ε), only two viralload markers are needed to complete the parameterization of the VDC.This is in contrast to previous techniques whereby expensive andlaborious techniques are required to determine the shape of a viraldiffusion curve. The present invention succeeds in using only two viralload markers in most cases by exploiting the canonical VDC describedabove which has predefined properties and which is predetermined basedupon the particular biochip being used.

Calibration of Viral Diffusion Curves

Referring again to FIG. 1, the directional causality of the VDC iscalibrated at step 104 in the context of an NIF discussed in greaterdetail below. At least arbitrarily selected three sample points are usedexecute the NIF calibration computation. The resulting polynomial isused to extracting qualitative coherence properties of the system.

The spectral [Θ] and temporal coherence [] is incrementally estimatedand computed for each mutation/oligonucleotide of interest by a NIFforward estimation computation (described further below). The twoestimates are normalized and convolved to yield cross-correlationfunction over time. The shape index (i.e., curvature) of the minima isused as a measure for directional causality. Absence of curvaturedivergence is used to detect high directional causality in the system.

Sample Collection

Samples are collected at step 106 subject to a sample point collectionseparation amount. The separation amount for two samples is preferablywithin half a “drug effectiveness mean time” covering 2σ populationlevel wherein σ denotes the standard deviation in period before which aeffectiveness for a particular drug is indicated. The following are somegeneral guidelines for sample preparation for use with the exemplarymethod:

It is important that assay specimen requirements be strictly followed toavoid degradation of viral RNA.

A baseline should be established for each patient with two specimensdrawn two to four weeks apart.

Patients should be monitored periodically, every three to four months ormore frequently if therapy is changed. A viral load level that remainsat baseline or a rising level indicates a need for change in therapy.

Too much significance should not be given to any one viral load result.Only sustained increases or decreases of 0.001-0.01 log [conventionalmethods typically require a 0.3-0.5 log change] or more should beconsidered significant. Biological and technical variation of up to 0.01log [typical conventional limit: 0.3 log] is possible. Also, recentimmunization, opportunistic infections and other conditions may causetransient increases in viral load levels.

A new baseline for each patient should be established when changinglaboratories or methods.

Recommendations for frequency of testing are as follows:

establish baseline: 2 measurements, 2 to 4 weeks apart

every 3 to 4 months or in conjunction with CD4⁺ T-cell counts

3 to 4 weeks after initiating or changing antiretroviral therapy

shorter intervals as critical decisions are made.

measurements 2-3 weeks apart to determine a baseline measurement.

repeat every 3-6 months thereafter in conjunction with CD4 counts tomonitor viral load and T-cell count.

avoid viral load measurements for 3-4 weeks following an immunization orwithin one month of an infection.

a new baseline for each patient should be established when changinglaboratories or methods.

The samples are applied to a prefabricated DNA biomicroarray to generateone or more dot spectrograms each denoted Φ(i,j) for i:1 to N, and j:1to M. The first sample is referred to herein as the k=1 sample, thesecond as the k=2 sample, and so on.

Interferometric Enhancement of the Dot Spectrogram

Each dot spectrogram provided by the DNA biomicroarray is filtered atstep 108 to yield enhanced dot spectrograms Φ(κ) either by performing aconventional Nucleic Assay Amplification or by applying preconditioningand normalization steps as described in the co-pending patentapplication having Ser. No. 09/253,789, now U.S. Pat. No. 6,136,541,entitled “Method And Apparatus For Analyzing Hybridized Biochip PatternsUsing Resonance Interactions Employing Quantum Expressor Functions”. Theapplication is incorporated by reference herein, particularly insofar asthe descriptions of the use of preconditioning and normalization curvesare concerned.

Fractal Filtering

Each enhanced dot spectrogram is then mapped to the VDC using fractalfiltering at step 110 as shown in FIG. 3 by generating a partitionediterated fractal system 302, determining affine parameters for the IFS304 and then mapping the enhanced dot spectrogram onto the VDC using theIFS, step 306.

The VDC representation models a stochastic process given by${{W(f)}\left( {x,y} \right)} = \left\{ \begin{matrix}{{\gamma_{i} \cdot {f\left( {{\frac{1}{\sigma_{i}}\left( \frac{x - x_{D}^{i}}{y - y_{D}^{i}} \right)} + \frac{x_{R}^{i}}{y_{R}^{i}}} \right)}} + {\tau \left( \frac{x - x_{D}^{i}}{y - y_{D}^{i}} \right)} + \beta_{i,}} \\{{{{if}\quad \left( {x,y} \right)} \in {\mu_{i}^{- 1}(1)}},{{{{for}\quad {some}\quad 1} \leq i \leq m};}} \\{0,{{\text{~~~~~~~~~~}{otherwise}};}}\end{matrix} \right.$

for any (x,y)∈R² and f ∈p (R²)

An exemplary partitioned iterated fractal system (IFS) model for thesystem is

W={Φ_(i)=(μ_(i),T_(i))}i=1,2, . . . , m

where the affine parameters for the IFS transformation are given by$T_{i} = \left( {\left( {x_{D}^{i},y_{D}^{i}} \right),\left( {x_{R}^{i},y_{R}^{i}} \right),{\sigma_{i} = \begin{pmatrix}s_{00}^{i} & s_{01}^{i} \\s_{10}^{i} & s_{11}^{i}\end{pmatrix}},{\tau_{i} = \left( {t_{0}^{i},t_{1}^{i}} \right)},{\gamma_{i,}\beta_{i,}}} \right)$

where the D-origin is given by (x^(i) _(D), y^(i) _(D)),

the R-origin is given by (x^(i) _(R), y^(i) _(R))

spatial transformation matrix is given by σ_(i)

the intensity tilting vector is given by τ_(i)

the contrast adjustment is given by γ_(i),

the brightness adjustment is given by β_(i),

and wherein Φ represents the enhanced dot spectrogram and wherein μrepresents the calculated expectation match values.

This IFS model maps the dot spectrogram to a point on the VDC whereineach VDC coordinate is denoted by VDC(t,Θ) such that

W[Φ, k]→VDC (k, Θ)

Wherein k represents a sample.

In the above equation, Θ represent the parameters of the IFS map.

Thus the output of step 110, is a set of VDC coordinates, identified asVDC(k, Θ), with one set of coordinates for each enhanced dot spectrogramk=1, 2. . . n.

The effect of the steps of FIG. 3 is illustrated in FIG. 4 which shows aset of dot spectrograms 450, 451 and 452 and a VDC 454. As illustrated,each dot spectrogram is mapped to a point on the VDC. Convergence towarda single point on the VDC implies ineffectiveness of the viral therapy.A convergence test is described below.

Uncertainty Compensation

With reference to FIG. 5, any uncertainty in the coordinates VDC(k, Θ)is compensated using Non-linear Information Filtering as follows.Biomicroarray dispersion coefficients, hybridization process variabilityvalues and empirical variance are determined at step 402. Thebiomicroarray dispersion coefficients, hybridization process variabilityvalues and empirical variance are then converted at step 404 toparameters for use in NIF. The NIF is then applied at step 406 to theVDC coordinates generated at step 106 of FIG. 1.

Nonlinear information filter (NIF), is a nonlinear variant of theExtended Kalman Filter. A nonlinear system is considered. Linearizingthe state and observation equations, a linear estimator which keepstrack of total state estimates is provided. The linearized parametersand filter equations are expressed in information space. This gives afilter that predicts and estimates information about nonlinear stateparameters given nonlinear observations and nonlinear system dynamics.

The information Filter (IF) is essentially a Kalman Filter expressed interms of measures of the amount of about the parameter of interestinstead of tracking the states themselves, i.e., track the inversecovariance form of the Kalman filter. Information here is in the Fishersense, i.e. a measure of the amount of information about a parameterpresent in the observations.

Uncertainty bars are estimated using NIF algorithm. The parametersdepend on biomicroarray dispersion coefficients, hybridization processvariability and empirical variance indicated in the trial studies.

One particular advantage of the method of the invention is that it canalso be used to capture the dispersion from individual to individual,therapy to therapy etc. It is extremely useful and enabling to themethod in that it can be apriori analytically set to a prechosen valueand can be used to control the quality of biomicroarray output mappingto VDC coordinates.

The biomicroarray dispersion coefficients, hybridization processvariability values and empirical variance are determined as follows.Palm generator functions are used to capture stochastic variability inhybridization binding efficacy. This method draws upon results instochastic integral geometry and geometric probability theory.

Geometric measures are constructed to estimate and bound the amplitudewanderings to facilitate detection. In particular we seek a measure foreach mutation-recognizer centered (MRC-) hixel that is invariant tolocal degradation. Measure which can be expressed by multiple integralsof the form m(Z) = ∫_(Z)f(z)z

where Z denotes the set of mutations of interest. In other words, wedetermine the function f(z) under the condition that m(z) should beinvariant with respect to all dispersions ξ. Also, up to a constantfactor, this measure is the only one which is invariant under a group ofmotions in a plane. In principle, we derive deterministic analyticaltransformations on each MRC-hixel., that map error-elliptic dispersionbound defined on R² (the two dimension Euclidean space—i.e., oxellayout) onto measures defined on R. The dispersion bound is given by

Log₄(Ô_((i,j))|^(z)).

Such a representation of uniqueness facilitates the rapid decimation ofthe search space. It is implemented using a filter constructed usingmeasure-theoretic arguments. The transformation under consideration hasits theoretical basis in the Palm Distribution Theory for pointprocesses in Euclidean spaces, as well as in a new treatment in theproblem of probabilistic description of MRC-hixel dispersion generatedby a geometrical processes. Latter is reduced to a calculation ofintensities of point processes. Recall that a point process in someproduct space E X F is a collection of random realizations of that spacerepresented as {(e_(i), f_(i)), |e_(I)∈E, f_(i) ∈F}.

The Palm distribution, Π of a translation (T_(n)) invariant, finiteintensity point process in R^(n) is defined to the conditionaldistribution of the process. Its importance is rooted in the fact thatit provides a complete probabilistic description of a geometricalprocess.

In the general form, the Palm distribution can be expressed in terms ofa Lebesgue factorization of the form

E_(p)N*=ΛL_(N)XΠ

Where Π and Λ completely and uniquely determine the source distributionP of the translation invariant point process. Also, E_(p) N* denotes thefirst moment measure of the point process and L_(N) is a probabilitymeasure.

Thus a determination of Π and Λ is needed which can uniquely encode thedispersion and amplitude wandering associated with the MRC-hixel. Thisis achieved by solving a set of equations involving Palm Distributionfor each hybridization (i.e., mutation of interest). Each hybridizationis treated as a manifestation of a stochastic point process in R².

In order to determine Π and Λ we have implemented the followingmeasure-theoretic filter:

Determination of Λ

using integral formulae constructed using the marginal density functionsfor the point spread associated with MRC-hixel(i,j)

The oligonucleotide density per oxel ρ_(m(i,j)), PCR amplificationprotocol (σ_(m)), fluorescence binding efficiency (η_(m)) and imagingperformance ({tilde over (ω)}_(m)) provide the continuous probabilitydensity function for amplitude wandering in the m-th MRC-hixel ofinterest. Let this distribution be given by p(ρ_(m(i,j)), σ_(m), η_(m),{tilde over (ω)}_(m)).

The method requires a preset binding dispersion limit to be provided tocompute Λ. The

p(ρ_(m(i,j)), σ_(m), η_(m), {tilde over (ω)}_(m))

second moment to the function

at SNR=0 condition is used to provide the bound.

Determination of Π.

Obtained by solving the inverse problem

Π=Θ* P

where P = ∫_(τ₁)^(τ₂)℘  (ρ_(m(i, j)), σ_(m), η_(m), ϖ_(m))∂τ

where τ₁ and τ₂ represent the normalized hybridization dispersionlimits.

The number are empirically plugged in. The values of 0.1 and 0.7 areappropriate for, respectively, signifying loss of 10%-70% hybridization.Also , Θ denotes the distribution of known point process. The form1/(1+exp(p( . . . ))) is employed herein to represent Θ.

The biomicroarray dispersion coefficients, hybridization processvariability values and empirical variance are then converted toparameters at step 304 for use in NIF as follows.

The NIF is represented by:

Predicted State=f(current state, observation model, informationuncertainty, information model)

Detailed equations are given below.

In the biomicroarray context, NIF is an information-theoretic filterthat predicts and estimates information about nonlinear state parameters(quality of observable) given nonlinear observations (e.g., posthybridization imaging) and nonlinear system dynamics (spatio-temporalhybridization degradation). The NIF is expressed in terms of measures ofthe amount of information about the observable (i.e., parameter ofinterest) instead of tracking the states themselves. It has been definedas the inverse covariance of the Kalman filter, where the information isin the Fisher sense, i.e, a measure of the amount of information abouto_(l) present in the observations Z^(k) where the Fisher informationmatrix is the covariance of the score function.

In a classical sense the biomicroarray output samples can be describedby the nonlinear discrete-time state transition equation of the form:

VDC(k)=f(VDC(k−1), Φ(k−1),k)+v(k)

where VDC(k−1) is the state at time instant (k−1),

Φ(k−1) is the input vector (embodied by dosage and/or therapy)

v(k) is some additive noise; corresponds to the biomicroarray dispersionas computed by the Palm Generator functions above.

VDC(k) is the state at time k,

f(k, . ,) is the nonlinear state transition function mapping previousstate and current input to the current state. In this case it is thefractal mapping that provides the VDC coordinate at time k.

The observations of the state of the system are made according to anon-linear observation equation of the form

z(k)=h(VDC(k))+w(k)

where z(k) is the observation made at time k

VDC(k) is the state at time k,

w(k) is some additive observation noise

and h(.,k) is the current non-linear observation model mapping currentstate to observations, i.e., sequence-by-hybridization made at time k,

v(k) and w(k) are temporally uncorrelated and zero-mean. This is truefor the biomicroarray in how protocol uncertainties, binding dynamicsand hybridization degradation are unrelated and additive. The processand observation noises are uncorrelated.

E[v(i)w ^(T)(j)]=0, ∀i,j.

The dispersion coefficients together define the nonlinear observationmodel.

The nonlinear information prediction equation is given by

ŷ(k|k−1)=Y(k|k−1)f(k,{circumflex over (V)}DC(k−1|k−1),u(k−1))

Y(k|k−1)=└∇f _(x)(k)Y ⁻¹(k−1|k−1)∇f _(x) ^(T)(k)+Q(k)┘⁻¹

The nonlinear estimation equations are given by

ŷ(k|k)=ŷ(k|k−1)+i(k)

Y(k|k)=Y(k|k−1)+I(k)

where

I(k)=∇h _(x) ^(T)(k)R ⁻¹(k) ∇h _(x)(k)

i(k)=∇h _(x) ^(T)(k)R ⁻¹(k) [v(k)+∇h _(x)(k) {circumflex over(V)}DC(k|k−1)]

where

v(k)=z(k)−h({circumflex over (x)}(k|k−1)).

In this method NIF helps to bind the variability in the VDC coordinatemapping across sample to sample so that dosage and therapy effectivenesscan be accurately tracked.

The NIF is then applied to enhanced, fractal-filtered dot spectrogram atstep 306 as follows. States being tracked correspond topost-hybridization dot spectrogram in this method. NIF computation asdescribed above specifies the order interval estimate associated with aVDC point. It will explain and bound the variability in Viral loadestimations for the same patient from laboratory to laboratory.

The NIF also specifies how accurate each VDC coordinate is given theobservation model and nucleotide set being analyzed.

Convergence Testing

Referring again to FIG. 1, once any uncertainty is compensated, the VDCcoordinates are renormalized at step 114. The renormalized VDCcoordinates are patient specific and therapy specific. Alternately thecoordinates could be virus/nucleotide marker specific. TheNIF-compensated VDC coordinates are renormalized to the first diagnosticsample point obtained using the biomicroarray. Thus a patient can bereferenced to any point on the VDC.

This renormalization step ensures that VDC properties are maintained,notwithstanding information uncertainties as indicated by the NIFcorrection terms. The approach is drawn from “renormalization-group”approach used for dealing with problems with many scales. In general thepurpose of renormalization is to eliminate an energy scale, length scaleor any other term that could produce an effective interaction witharbitrary coupling constants. The strategy is to tackle the problem insteps, one step for every length scale. In this method therenormalization methodology is abstracted and applied during aposteriori regularization to incorporate information uncertainty andsample-to-sample variations.

This is in contradistinction to current viral load measurementcalibration methods that either generate samples with same protocol andsame assumptions of uncertainty or use some constant correction term.Both existing approaches skew the viral load readout so thatmeasurements are actually accurate only in a limited “information” and“observability” context. This explains the large variations in readingsfrom different laboratories and technicians for the same patient sample.

Specifically, we include the dynamic NIF correction function to thegradient of the VDC at the sample point normalized in a manner such thatwhen the information uncertainty is null, the correction term vanishes.As discussed in the above steps, the NIF correction terms is actuallyderived from the noise statistics of the microarray sample.

<VDC′(k,Θ)>=VDC(k,Θ)+[∇NIF(Y,I)_(k)]

where ∇NIF(Y,I)_(k) denotes the gradient of nonlinear informationprediction function. Under perfect observation model this term vanishes.

Once initialized, the VDC coordinates are then updated at step 116applying the IFS filter W[ ] on k+1th sample, by

VDC(k+1, Θ)←W[Biomicroarray Output, K+1];

A direction convergence test is next performed at step 118 to determinewhether the selected therapy has been effective. If convergenceestablishes that the viral load for the patient is moving in a directionrepresentative of a lower viral load, then the therapy is deemedeffective. The system is deemed to be converging toward a lower viralload if and only if:${\frac{{{VDC}\left( t_{k} \right)} - {{VDC}\left( t_{k - j} \right)}}{{{VDC}\left( t_{k - 1} \right)} - {{VDC}\left( t_{k - j} \right)}}} > {1\bigwedge{\frac{{VDC}_{peak} - {{VDC}\left( t_{k} \right)}}{{VDC}_{peak} - {{VDC}\left( t_{k - 1} \right)}}}} < 1$for  k > 2  and  j > 0

The above relationships needs to be monotonically persistent for atleast two combinations of k and j.

Also, date[k]-date[j]<κ* characteristic time, {haeck over (t)} (in days)

Where κ captures the population variability. Typically, κ<1.2.

The peak VDC value is determined based on the VDC. The peak amplitude isan artifact of the specific parameterization to the Fokker-Planckequation used in deriving the VDC. It is almost always derivedindependent of the specific sample.

In connection with step 118, a VDC Shift factor Δ may be specified atwhich a dosage effectiveness decision and/or disease progressiondecision can be made. The VDC shift factor is applied to estimate theVDC curvature traversed between two measurements.

If the system is deemed to be converging toward a lower viral load, anoutput signal is generated indicating that the therapy of interest iseffective at step 120. If not, then the execution proceeds to step 122wherein VDC scale matching is performed. A key assumption underlyingthis method is that movement along VDC is significant if and only if thesample points are with a constant multiple of temporal scalecharacterizing the VDC. This does not in any way preclude thepharmacological relevance associated with the datapoints. But completepharmacological interpretation of the sample points is outside the scopeof this method. The process is assumed to be cyclostationary or at alarge time scale and two or more sample points have been mapped to VDCcoordinates. The coordinates are then plugged into an analytic toestimate the empirical cycle time ({haeck over (t)}). This isimplemented as described in the following sections.

Again the empirical cycle time ({haeck over (t)}) is used to establishdecision convergence.

Scale Matching

Select a forcing function of the form:

Ψ=k. p^(m) cos ωt

where k is a constant and m is a small odd integer (m<7).

The phase space for this dynamical system is represented by:$\overset{.}{x} = {\gamma \quad {\sin \left\lbrack {\frac{\sqrt{\omega}}{\alpha}{erf}\quad {m\left( \frac{x}{\sigma \sqrt{2}} \right)}} \right\rbrack}^{\frac{k}{k + 2}}\sin \quad \omega \quad t}$where ${{erf}\quad {m(x)}} = \left\{ \begin{matrix}{- 1} & {{{if}\quad x} < {- N}} \\{{erf}\quad (x)} & {{{if}\quad {x}} \leq N} \\1 & {x > N}\end{matrix} \right.$

and erf m(.) denotes the error function.

K is set to 1; where o<α, γ, ω<1 are refer to constants.

Let τ_(emp) denote the cycle-time-scale for this empirical system.

If log_(e)(τ_(emp)/T)>1 (in step 10) then we claim that time-scales donot match.

Time Scale Testing

Next a determination has been made as to whether an effectivenesstimescale has been exceeded at step 124 by:

Checking if a time step between successive sampling has exceeded T by

determining if Time_(k+1)−Time_(k)>T

such that VDC(k+1, Θ)−VDC(k, Θ)<ζ where

is set to 0.0001 and wherein

T is given by$T^{*} = {\frac{1}{\omega}{\arccos \quad\left\lbrack {1 - {\frac{B\left( {{1/3},{1/3}} \right)}{\sqrt[3]{2}}\frac{\alpha \sqrt{\omega}}{\gamma}}} \right\rbrack}}$

B(1/3,1/3) represents the Beta function around the coordinates(1/3,1/3), We can actually use all B(1/2i+1,1/2i+1) for i>1 and i<7.

If Time_(k+1)−Time_(k)>T then output signal at step 126 indicating thateither

no change in viral load concluded, OR

therapy deemed ineffective, OR

dosage deemed suboptimal.

If Time_(k+1)−Time_(k)<T then process another sample by repeating allsteps beginning with Step 4 wherein a dot spectrogram is generated for anew sample.

If the effectiveness time scale has been exceeded then a signal isoutput indicating that no determination can be as to whether the therapyof interest is effective. If the time scale is not exceeded, thenexecution returns to step 106 for processing another sample. Ifavailable, and the processing steps are repeated.

Alternative Implementations

Details regarding a related implementation may be found in co-pendingU.S. patent application Ser. No. 09/253,792, now U.S Pat. No. 6,142,681,filed contemporaneously herewith, entitled “Method and Apparatus forInterpreting Hybridized Bioelectronic DNA Microarray Patterns Using SelfScaling Convergent Reverberant Dynamics”, and incorporated by referenceherein.

The exemplary embodiments have been primarily described with referenceto flow charts illustrating pertinent features of the embodiments. Eachmethod step also represents a hardware or software component forperforming the corresponding step. These components are also referred toherein as a “means for” performing the step. It should be appreciatedthat not all components of a complete implementation of a practicalsystem are necessarily illustrated or described in detail. Rather, onlythose components necessary for a thorough understanding of the inventionhave been illustrated and described in detail. Actual implementationsmay contain more components or, depending upon the implementation, maycontain fewer components.

The description of the exemplary embodiments is provided to enable anyperson skilled in the art to make or use the present invention. Variousmodifications to these embodiments will be readily apparent to thoseskilled in the art and the generic principles defined herein may beapplied to other embodiments without the use of the inventive faculty.Thus, the invention is not intended to be limited to the embodimentsshown herein but is to be accorded the widest scope consistent with theprinciples and novel features disclosed herein.

What is claimed is:
 1. A technique for determining viral load within apatient sample applied to an arrayed information structure, where thearrayed information structure has a plurality of elements that emit dataindicative of viral load, based on digitized output patterns from thearrayed information structure, comprising the steps of:interferometrically enhancing the output patterns to cause interferencebetween the output patterns and a reference wave; and analyzing theinterferometrically enhanced output patterns to identify data indicativeof viral load to determine viral load.
 2. The technique of claim 1wherein the interferometric enhancement comprises the step of: inducingresonances based on interference between an expressor function andspectral characteristics of the output patterns; and wherein theanalysis step comprises the step of detecting the resonances, if any, ateach element in the interferometrically enhanced output patterns fromthe arrayed information structure.
 3. The technique of claim 2 whereinthe interferometric enhancement further includes the step tessellatingthe interferometrically enhanced output patterns prior to the inductionof resonances.
 4. The technique of claim 2 wherein and expressorfunction is a chosen from a group comprising: stochastic expressorfunctions, quantum expressor functions.
 5. The technique of claim 2wherein the spectral characteristics are selected from a groupcomprising: noise, signal, and noise coupled to signal.
 6. The techniqueof claim 2 further including the initial steps of generating a set ofnonlinear expressor functions by: calculating values representative of apre-selected Hamiltonian function; calculating harmonic amplitudes forthe Hamiltonian function; generating an order function from theHamiltonian; function measuring entrainment states of the orderfunction; and modulating the order function using the entrainment statesto yield the expressor function.
 7. The technique of claim 2 wherein thearrayed information structure is a microarray.
 8. The technique of claim1 wherein the arrayed information structure embodies measurementsselected from a group comprising: intensity, amplitude, and phase. 9.The technique of claim 1 wherein the analysis step comprises the step ofmapping the interferometrically enhanced output pattern to coordinateson a viral diffusion curve.
 10. The technique of claim 9 wherein themapped coordinates are non-linearly filtered.
 11. A system fordetermining viral load within a digitized image of a biological samplemeasurement taken from a microarray comprising: an interferometric unitconfigured to generate an interference between the digitized image and areference wave to enhance the digitized image; and an analysis unit foranalyzing the interferometrically enhanced digitized image to determineviral load.
 12. The system of claim 11, wherein said interferometricunit is configured to induce resonances based on interference between anexpressor function and spectral characteristics of the digitized image.13. The system of claim 12, wherein said analysis unit is configured todetect resonances, if any, within the interferometrically enhanceddigitized image that are associated with viral load.
 14. The system ofclaim 12 wherein and expresser function is chosen from a groupcomprising: stochastic expresser functions, quantum expressor functions.15. The system of claim 11 wherein said interferometric unit tessellatesthe digitized image of the output pattern prior to generating aninterference between the digitized image and a reference wave.
 16. Thesystem of claim 11 wherein the digitized image embodies measurementsfrom a group comprising: intensity, amplitude, phase.
 17. The system ofclaim 11 wherein the analysis unit maps the interferometrically enhanceddigitized image to a viral diffusion curve.
 18. The system of claim 11wherein the analysis unit maps the interferometrically enhanceddigitized image to a viral diffusion curve using fractal filtering. 19.A system for determining the level of a biological indicator within apatient sample applied to an arrayed information structure, where thearrayed information structure emits data indicative of the biologicalindicator, based on digitized images of the arrayed informationstructure, comprising: signal processing means for generatinginterference between the digitized image and a reference wave to enhancethe digitized image; and analysis means for analyzing the enhanceddigitized image to determine the level of the biological indicator. 20.A system for determining the level of a biological indicator within apatient sample applied to an arrayed information structure, where thearrayed information structure emits data indicative of the biologicalindicator, based on digitized output patterns from the arrayedinformation structure, comprising: an interferometric unit configured togenerate an interference between the digitized image and a referencewave to enhance the digitized output pattern; and an analysis unit foranalyzing the interferometrically enhanced digitized output pattern todetermine the level of the biological indicator.
 21. A system fordetermining the level of a biological indicator within a patient sampleapplied to an arrayed information structure, where the arrayedinformation structure emits data indicative of the biological indicator,based on digitized output patterns from the arrayed informationstructure, comprising: an interferometric unit configured to generate aninterference between the digitized output pattern and a reference waveto enhance the digitized output pattern; and an analysis unit foranalyzing the interferometrically enhanced digitized output pattern todetermine the level of the biological indicator.